Developments in the Theory of the Quantum Hall Effect, Proceedings of the 1994 Vancouver Semiconductor Conference

TL;DR

This paper reviews recent theoretical advances in understanding the quantum Hall effects, including fermion-Chern-Simons models, edge excitations, phase transitions, tunneling phenomena, and disorder effects, providing a comprehensive overview of the field.

Contribution

It summarizes new theoretical frameworks and insights that explain and predict phenomena in quantum Hall systems, especially at fractional and even-denominator filling fractions.

Findings

Fermion-Chern-Simons theories explain non-quantized Hall states.

Edge-excitation theories enhance understanding of fractional states.

Disorder-induced transitions between quantum Hall plateaus are characterized.

Abstract

The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting with a Chern-Simons gauge field, have been useful for explaining and predicting observations at even-denominator filling fractions where quantized Hall plateaus are not observed, as well as for giving new insight into the most prominent fractional quantized Hall states at odd-denominator fractions. Other theoretical approaches have led to important advances in our understanding of edge-excitations for systems in a fractional quantized Hall state, of phases and phase transitions in bilayer systems, of tunneling phenomena in the quantum Hall regimes, and of disorder-induced transitions between ``neighboring'' quantum Hall plateaus. Some highlights of these developments will be reviewed.